Sentence examples for satisfied the unique from inspiring English sources

Since all the conditions of Theorem 4.2 are satisfied, the unique endemic equilibrium (E^{ast }) is globally asymptotically stable in Δ.

And if R 01 and R 02 are above unity, and further S 2 1 ∗ > S 2 2 ∗ and S 1 2 ∗ > S 1 1 ∗ are satisfied, the unique endemic equilibrium is globally asymptotically stable by constructing the Lyapunov function.

Tetragonal Heusler compounds could thus satisfy the unique requirements of materials for STT-based memory and logic devices, and also for spin torque oscillators (STO) currently being investigated for telecommunications.

If condition (13) is satisfied, the equilibrium is unique and locally stable.

All the conditions of Theorem 3.1 are satisfied, and the unique positive equilibrium (E(x^_{1},x^_{2})) is globally attractive.

If relations (39) are satisfied, then the unique positive equilibrium ((overline {y},overline{z})) is globally asymptotically stable.

Consider the system of difference equations (34), if p>1,qquad q>1,qquad sqrt{3}pq>max{3p-q,3q-p} (39) are satisfied, then the unique positive equilibrium point ((overline{y},overline {z})) is locally asymptotically stable.

If on the other hand the input current does depend upon these variables is invariant under the action of a subgroup of U ( 1, 1 ) the group of the isometries of D (see Appendix A), and the condition μ S m ′ W 0 g < α is satisfied then the unique stationary solution will also be invariant under the action of the same subgroup.

Moreover, if the condition (2.2) is satisfied, the fixed point is unique.

Since all the conditions of Corollary 3.4 are satisfied, the mapping T has a unique fixed point (x=0) in Z.

First of all, if the conditions (H1) and (H2) are satisfied, the system (5.1) admits a unique mild solution in X for each control function (u x,t)) from Theorem 3.1.